Purpose: The present paper aims to explore how to measure trust as a receptivity force in an intra-organisational knowledge-sharing network with the help of self-developed algorithms of modelling percolations. Design/methodology/approach: In this paper, a completely new methodology is applied by using a sample study of an international company’s financial centre as an example. Computer software has been developed to simulate the network and calculate the percolation thresholds by combining its characteristics, thereby revealing what and to what extent connectivity and trust, respectively, influence knowledge sharing. Findings: The application of computer modelling to build up a percolation network is useful for answering questions about the determinants of knowledge sharing. Arguably, the authors demonstrate how the applied new methodology is superior in addressing how to measure the critical values of trust, connectivity and interaction issues, as well as leading to better insights about how these can be managed. The present paper confirms that trust is an essential factor influencing knowledge sharing and that there is a reciprocal effect between social interaction and trust. Practical implications: The model provides a useful tool for assessing features of the intra-organisational knowledge-sharing network and thus an important foundation for implementing actions in practice. The findings of this study imply that managers should consider the important role of task-related trust between actors and in general for knowledge sharing. With the help of percolation modelling, the degree of trust in an organisation can be computed, and this provides managers with an approach for managing trust. Originality/value: The topic of “how can trust be measured” is very important and is becoming even more important now because the financial crisis and other issues are raising questions about trust and moral compass rather than financial data. A percolation-based approach to studying knowledge sharing has not been researched in depth before now, and this study attempts to fill that gap. Fundamentally, this multidisciplinary research adds value to the theoretical foundation of the percolation network and research methodology to be used in social sciences and gives an example of their potential practical implications.

The directions of perspective research in the field of analysis and modeling of the dynamics of time series of processes in complex systems with the presence of the human factor are described. The dynamics of processes in such systems is described by nonstationary time series. Predicting the evolution of such systems is of great importance for managing processes in social (election campaigns), economic (stock, futures and commodity markets) and socio-technical systems (social networks). The general information on time series and tasks of their analysis is given. Modern methods of time series analysis for economic processes are considered. The results show that economic processes cannot be considered completely random, since they tend to self-organize and, moreover, are subject to the influence of memory of previous states. It was revealed that one of the main tasks in modeling processes in sociotechnical systems (for example, social networks) is the development of a mathematical apparatus for bringing data to a single measurement scale. The modern models of analysis and forecasting of electoral processes based on the analysis of time series: structural, polling, hybrid. Based on the analysis, their advantages and disadvantages are considered. In conclusion, it was concluded that to describe processes in complex systems with the presence of the human factor, in addition to traditional factors, it is necessary to develop and use methods and tools to take into account the possibility of self-organization of human groups and the presence of memory about previous states of the system.

Analyses of the processes of information transfer within network structures shows that the conductivity and percolation threshold of the network depend not only on its density (average number of links per node), but also on its spatial symmetry groups and topological dimension. The results presented in this paper regarding conductivity simulation in network structures show that, for regular and random 2D and 3D networks, an increase in the number of links (density) per node reduces their percolation threshold value. At the same network density, the percolation threshold value is less for 3D than for 2D networks, whatever their structure and symmetry may be. Regardless of the type of networks and their symmetry, transition from 2D to 3D structures engenders a change of percolation threshold by a value exp{−(d − 1)} that is invariant for transition between structures, for any kind of network (d being topological dimension). It is observed that in 2D or 3D networks, which can be mutually transformed by deformation without breaking and forming new links, symmetry of similarity is observed, and the networks have the same percolation threshold. The presence of symmetry axes and corresponding number of symmetry planes in which they lie affects the percolation threshold value. For transition between orders of symmetry axes, in the presence of the corresponding planes of symmetry, an invariant exists which contributes to the percolation threshold value. Inversion centers also influence the value of the percolation threshold. Moreover, the greater the number of pairs of elements of the structure which have inversion, the more they contribute to the fraction of the percolation threshold in the presence of such a center of symmetry. However, if the center of symmetry lies in the plane of mirror symmetry separating the layers of the 3D structure, the mutual presence of this group of symmetry elements do not affect the percolation threshold value. The scientific novelty of the obtained results is that for different network structures, it was shown that the percolation threshold for the blocking of nodes problem could be represented as an additive set of invariant values, that is, as an algebraic sum, the value of the members of which is stored in the transition from one structure to another. The invariant values are network density, topological dimension, and some of the elements of symmetry (axes of symmetry and the corresponding number of symmetry planes in which they lie, centers of inversion).

To describe the structure of news information domain, we introduce the concept of a director, that is a conditional axis, the position of which is defined by averaging the directions of vectors that set the location of all news clusters centroids. To characterise the dynamics of reaching the news event, we introduce the concepts of decreasing and increasing trends of domain varying. The analysis of self-similarity in behaviour of directors and trends on the basis of the proposed model can allow detecting the periodicity of domain approaching or moving away from the point of the predicted event.

The paper expands on the elaborated model of forecasting news events basing on the stochastic dynamics of news clusters variance and memory-based realisation in an information domain with self-organizing poorly structured data. The provided analysis of stochastic dynamics in overcoming the news events threshold shows the transition probability appearing right after the process of changing the news clusters dimensions and structure begins. The allowances for the second time derivative in the differential model of information process enable accounting for the memory of the previous states of the information system and the possibility to describe the system's considerable self-organisation. Basing on the developed model, the authors have designed an algorithm of analysing the interrelations of news clusters in the information domain with a probability for a forecast event happening, and defining a possible time of its occurrence.

В работе представлена комплексная модель динамики развития эпидемий вирусов в компьютерных сетях, созданная на основе учета их топологических свойств и механизмов распространения вирусов. С одной стороны, данная модель основана на использовании методов теории перколяции, которые позволяют определить такие структурно-информационные характеристики сетей, как зависимость порога перколяции от среднего числа связей (приходящихся) на один узел (плотность сети). С другой стороны, рассматриваются динамические процессы стохастического распространения в компьютерных сетях эволюционирующих вирусов при устаревании и запаздывании действия антивирусов. В работе рассматривается понятие порога перколяции, приводится уравнение зависимости величины порога перколяции сети от её плотности, полученное в результате анализа данных численного моделирования. Динамика распространения вирусов разработана с использованием двух подходов: первый основан на описании диаграмм переходов между состояниями узлов, после чего строится система кинетических дифференциальных уравнений распространения вирусов; второй – на рассмотрении вероятностей переходов между возможными состояниями всей сети в целом. Получено дифференциальное уравнение второго порядка и сформулирована краевая задача, решение которой описывает зависимость вероятности блокирования сети от вероятности блокирования отдельного узла. Это решение позволяет также оценить время достижения порога перколяции. В модель заложены эволюционные свойства вирусов (ранее иммунизированные или вылеченные узлы через некоторый интервал времени могут быть снова инфицированы), и время запаздывания антивирусной защиты. Анализ полученных решений для созданных моделей показывает возможность существования различных режимов распространения вирусов. Подчеркнуть, что при некоторых наборах величин коэффициентов дифференциальных уравнений наблюдается осциллирующий и почти периодический характер распространения вирусных эпидемий, что в значительной степени совпадает с реальными наблюдениями.